On the remainder term of Gauss-Radau quadratures for analytic functions
Abstract
For analytic functions the remainder term of Gauss–Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points and a sum of semi-axes for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss–Lobatto and Gauss–Radau quadratures, Rocky Mountain J. Math. 21 (1991), 209–226] is proved.
Keywords:
Gauss–Radau quadrature formula / Chebyshev weight function / Error bound / Remainder term for analytic functions / Contour integral representationSource:
Journal of Computational and Applied Mathematics, 2008, 218, 2, 281-289Publisher:
- Elsevier
Funding / projects:
- Serbian Ministry of Science and Environmental Protection (Project #144005A: “Approximation of linear operators”)
Institution/Community
Mašinski fakultetTY - JOUR AU - Milovanović, Gradimir AU - Spalević, Miodrag AU - Pranić, Miroslav PY - 2008 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5086 AB - For analytic functions the remainder term of Gauss–Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points and a sum of semi-axes for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss–Lobatto and Gauss–Radau quadratures, Rocky Mountain J. Math. 21 (1991), 209–226] is proved. PB - Elsevier T2 - Journal of Computational and Applied Mathematics T1 - On the remainder term of Gauss-Radau quadratures for analytic functions EP - 289 IS - 2 SP - 281 VL - 218 UR - https://hdl.handle.net/21.15107/rcub_machinery_5086 ER -
@article{ author = "Milovanović, Gradimir and Spalević, Miodrag and Pranić, Miroslav", year = "2008", abstract = "For analytic functions the remainder term of Gauss–Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points and a sum of semi-axes for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss–Lobatto and Gauss–Radau quadratures, Rocky Mountain J. Math. 21 (1991), 209–226] is proved.", publisher = "Elsevier", journal = "Journal of Computational and Applied Mathematics", title = "On the remainder term of Gauss-Radau quadratures for analytic functions", pages = "289-281", number = "2", volume = "218", url = "https://hdl.handle.net/21.15107/rcub_machinery_5086" }
Milovanović, G., Spalević, M.,& Pranić, M.. (2008). On the remainder term of Gauss-Radau quadratures for analytic functions. in Journal of Computational and Applied Mathematics Elsevier., 218(2), 281-289. https://hdl.handle.net/21.15107/rcub_machinery_5086
Milovanović G, Spalević M, Pranić M. On the remainder term of Gauss-Radau quadratures for analytic functions. in Journal of Computational and Applied Mathematics. 2008;218(2):281-289. https://hdl.handle.net/21.15107/rcub_machinery_5086 .
Milovanović, Gradimir, Spalević, Miodrag, Pranić, Miroslav, "On the remainder term of Gauss-Radau quadratures for analytic functions" in Journal of Computational and Applied Mathematics, 218, no. 2 (2008):281-289, https://hdl.handle.net/21.15107/rcub_machinery_5086 .